From Kerbin circular orbit to back home by pointing straight down

[closette]

I did some calculations in another thread based on a rail-gun 'shooting' straight down at Kerbin from a high circular orbit,

http://kerbalspaceprogram.com/forum/index.php?topic=6396.msg85438#msg85438, and it suggested the following challenge:

The story is as follows. Our kerbonauts are in a high circular orbit with the spacecraft nose pointing directly at Kerbin\'s center. Suddenly they lose attitude control even though the gyro stabilizers still work. The only way to get home is to boost quickly downwards in that constant direction, and hope that their path will intersect Kerbin.

From a near circular orbit around Kerbin, point straight down at Kerbin\'s center, set SAS to fix that direction in space, then try to get back home by boosting in that direction only. What is the highest circular orbit from which you can do that?

Rules:

- all components must be 100% stock

- Once you\'ve set the initial downward direction, you cannot change it, e.g. to continuously point towards Kerbin, otherwise you could easily spiral inwards with enough time and fuel on your hands.

- No waiting around. You must start boosting when pointing straight down at Kerbin, and must complete the challenge in less than 1/4 of your original orbital period.

- You must stay in Kerbin\'s sphere of influence at all times from orbit to periapsis

- the initial circular orbit must have peri- and apokerb within 5% of each other. The perikerb altitude will count and be reported as your attempted orbit height.

- Achieving any periapsis below 30 000m is considered 'mission success'. (Edited, see reply 3)

- How you get up to orbit is up to you, but thanks to enviromentalists\' protests about orbital debris, NO jettisoning of any tanks or other solid items once you start the radial boost (i.e. any tanks you empty have to stay along for the ride), until you reach Kerbin\'s atmosphere.

- Acceptable proof consists of 2 pairs of screenshots - spacecraft view & map view (with Navball) just before boosting, and spacecraft view & map view (with Navball) just after achieving success or partial success. The spacecraft and map views should be within 2 minutes of each other. (We need the before and after spacecraft views to confirm that all the bits are still there).

I tried from 350 000 m altitude, it was easy. From 3 million m altitude I failed, but I didn\'t try very hard.

Screenshots attached of my failed attempt (sorry, not very good ones, but showing that I couldn\'t get periapsis low enough in time). Did I miss anything?

Suggestions (be nice!)? Remember, this is a 100% stock challenge, and it may be more suited for our newer kerbonauts.

[closette]

No takers yet? The environmentalists could be persuaded to relax the 'no jettison' condition on the challenge, if that helps.

[lars]

Does the SAS keep you actually keep you pointed towards the center? I would expect that half an orbit later you would be pointing straight up.

Also, I feel like a perigee below 70 km is full success because your kerbanauts still get home, but have a much more pleasantry entry as well.

[closette]

Hi lars,

The SAS will keep you pointing towards your original direction in space, think of it as a gyro stablizer when engaged. That\'s the challenging part about this challenge. If you can\'t accelerate radially fast enough, then after a while you\'ll be pointing 'off center' and will end up zooming past Kerbin, probably on an escape trajectory. And yes, half an orbit later you\'ll be pointing upwards, but you\'ll know you\'ve failed to get home long before then!

If you just keep pointing at Kerbin\'s center you can spiral inwards more easily and its less, well, challenging (although not trivial).

OK, perigee below 70 km altitude is success for the reasons you describe. I\'ll edit the original post to reflect that.

[closette]

Let\'s make that periapsis below 30km altitude, because I just tried the challenge myself from an 8.5 million meter orbit (but cheating by jettisoning lots of stages on the way in) to reach a perikerb of 40km altitude. I came screaming in on a hyperbolic path at > 4000 m/s and ended up screaming back out again!

I\'ve also come up with a dramatic back-story that some people seem to like with these challenges, which I shall include in the original post.

[lars]

I would just wait 3 quarters of an orbit until I am pointing opposite of my velocity vector. That is when the burn is most effective. Which should be legal according to your rules so it is not much different than a regular de-orbit in that sense.

[closette]

Haha, lars, I didn\'t think of that! You win. Well, not much interest in this challenge anyway, although it made me put some fairly powerful ships into orbit.

[Darkshadow]

Haha, lars, I didn\'t think of that! You win. Well, not much interest in this challenge anyway, although it made me put some fairly powerful ships into orbit.

I\'ll still attempt the challenge, there will still be some difficulty if you are not allowed to adjust your angle.

[Herra Tohtori]

Maybe they also have a life support failure that is connected to RCS failure, and they cannot wait that long to de-orbit...

[closette]

OK I\'ll keep the challenge up and add one more rule - no waiting around!

Yes, the fixed direction makes it more difficult for high orbits, even though you are moving more slowly out there. One explanation from a physics standpoint is that higher orbits have more angular momentum, which the constrained boosting direction can barely change, so to have the same angular momentum at a low periapsis means you have to add a bunch of orbital energy.